How can voters who casually follow politics be strongly influenced by those with a stake in how voters vote?
The kind of people you are talking about here are often called opinion leaders. They are the people who really care about the outcomes of elections and who pay the most attention to politics. Voters who casually follow politics can be affected by those people because they distill the issues for the voters and seem to be very sure of which side is right.
One of the major problems that casual voters face is the need to understand all of the complexities of the issues that are important to the country. Opinion leaders can make it easier for voters to feel that they know enough about those issues to vote one way or the other. Opinion leaders explain the issues to voters in ways that seem simple and obvious, thus making it clear how voters “should” vote.
By reducing the costs of obtaining information about candidates and issues, opinion leaders can strongly influence the actions of people who follow politics casually.